# Determining the Geometry Problem Posing Performances of Eighth Grade Students in Different Problem Posing Situations

**Abstract views:**153 /

**PDF downloads:**54

## DOI:

https://doi.org/10.33200/ijcer.575063## Keywords:

Geometry problem posing, Middle school students, Problem posing situations## Abstract

In this study, it was aimed to determine the geometry problem posing performance of eighth grade students in different problem posing situations. For this purpose, the convergent parallel mixed model accepted as one of the mixed method designs was preferred. The participants consisted of 151 eighth grade students from the same school. The “Geometry Problem Posing Test” was used as a data collection tool which consists of a total of six open-ended problems including free, semi-structured, and structured problem posing situations developed by the researchers. An analytical rubric including seven criteria was used for the analysis of the student posed problems. In the research, a significant difference was found among the problem posing situations. In order to examine this difference in depth, the rubric criteria were analysed descriptively with a qualitative approach. After the analysis, it was concluded that the success in structured problem posing situations was lower than the success in other problem posing situations. Therefore, it can be said that the structured problem posing situations can be more challenging for students in geometry problem posing.

## References

Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.

Abu-Elwan, R. (2011). Effect of using Cabri II environment by prospective teachers on fractal geometry problem posing. In M. Joubert, A. Clark-Wilson & M. McCabe (Eds.), Proceedings of the 10th International Conference for Technology in Mathematics Teaching (pp. 56-61). Portsmouth, UK.

Akkan, Y., Çakıroğlu, Ü., & Güven, B. (2009). İlköğretim 6. ve 7. sınıf öğrencilerinin denklem oluşturma ve problem kurma yeterlilikleri [Equation posing and problem posing abilities of 6th and 7th grade primary school students]. Mehmet Akif Ersoy University Journal of Education Faculty, 9(17), 41-55.

Arıkan, E. E., & Ünal, H. (2013). İlköğretim 2. sınıf öğrencilerinin matematiksel problem kurma becerilerinin incelenmesi [The analysis of mathematical problem posing skill of elementary second grade students]. Amasya Education Journal, 2(2), 305-325.

Atalay, Ö., & Güveli, E. (2017). İlkokul 4. sınıf öğrencilerinin kesirler konusunda bilgisayar animasyonları yardımıyla problem kurma becerilerinin incelenmesi [Examination of problem posing abilities using computer animations on fractions in the 4th grade students]. Adıyaman University Journal of Educational Sciences, 7(2), 192-220.

Bayazit, İ., & Kırnap-Dönmez, S. M. (2017). Öğretmen adaylarının problem kurma becerilerinin orantısal akıl yürütme gerektiren durumlar bağlamında incelenmesi [Prospective teachers’ proficiencies at problem posing in the context of proportional reasoning]. Turkish Journal of Computer and Mathematics Education, 8(1), 130-160.

Bonotto, C. (2013). Artifacts as sources for problem posing activities. Educational Studies in Mathematics, 83(1), 37-55.

Brown, S. I., & Walter, M. I. (2005). The art of problem posing, (3rd ed.). New York: Psychology Press.

Cai, J. (1998). An investigation of US and Chinese students' mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37-50.

Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.

Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401-421.

Cai, J., & Middleton J. (2015). Foreword. In F.M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. v–vi). New York (NY): Springer.

Cankoy, O., & Darbaz, S. (2010). Problem kurma temelli problem çözme öğretiminin problemi anlama başarısına etkisi [Effect of a problem posing based problem solving instruction on understanding problem]. Hacettepe University Journal of Education, 38, 11-24.

Cankoy, O., & Özder, H. (2017). Generalizability theory research on developing a scoring rubric to assess primary school students' problem posing skills. Eurasia Journal of Mathematics, Science and Technology Education, 13(6), 2423-2439.

Cansız-Aktaş, M., & Aktaş, D. Y. (2012). Öğrencilerin dörtgenleri anlamaları: Paralelkenar örneği [Students’ understanding of quadrilaterals: The sample of parallelogram]. Journal of Research in Education and Teaching, 1(2), 319-329.

Chang, K. E., Wu, L. J., Weng, S. E., & Sung, Y. T. (2012). Embedding game-based problem solving phase into problem posing system for mathematics learning. Computers & Education, 58(2), 775-786.

Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Mathematics Enthusiast, 2(2), 124-143.

Chua, P. H., & Wong, K. Y. (2012). Characteristics of problem posing of grade 9 students on geometric tasks. In J. Dindyal, L. P. Cheng & S. F. Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia). Singapore: MERGA.

Cifarelli, V. V., & Cai, J. (2006). The role of self-generated problem posing in mathematics exploration. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N. (Eds.), Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, (Vol.2 pp. 321-328). Prague: PME.

Creswell, J. W. (2014). Research design: qualitative, quantitative and mixed methods approaches (Fourth edition). Thousand Oaks: Sage.

Çarkçı, İ. (2016). İlkokul 4. sınıf öğrencilerinin farklı problem kurma durumlarına yönelik ortaya koydukları problemlerin incelenmesi [Investigation of the problems encountered by 4th grade primary students in different problem posing situations] (Unpublished master's thesis). Gazi University, Insitute of Education Sciences, Ankara.

Çelik, A., & Yetkin-Özdemir, E. (2011). İlköğretim öğrencilerinin orantısal akıl yürütme becerileri ile oran-orantı problemi kurma becerileri arasındaki ilişki [The relationship between elementary school students’ proportional reasoning skills and problem posing skills involving ratio and proportion]. Pamukkale University Journal of Education, 30(1), 1-11.

Dickerson, V. M. (1999). The impact of problem posing instruction on the mathematical problem solving achievement of seventh graders (Unpublished doctoral dissertation). University of Emory, Atlanta.

English, L. D. (1997). The development of fifth-grade children’s problem posing abilities. Educational Studies in Mathematics, 34, 183-217.

English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.

Fukuda, C., & Kakihana, K. (2009). Problem posing and its environment with technology. In Proceeding of 33rd conference of Japan Society for Science Education.

Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78-84.

Gökkurt, B., Örnek, T., Hayat, F., & Soylu, Y. (2015). Öğrencilerin problem çözme ve problem kurma becerilerinin değerlendirilmesi [Assessing students’ problem solving and problem posing skills]. Bartın University Journal of Faculty of Education, 4(2), 751-774.

Kaba, Y., & Şengül, S. (2016). Developing the rubric for evaluating problem posing (REPP). International Online Journal of Educational Sciences, 8(1), 8-25.

Kanbur, B. (2017). İlköğretim matematik öğretmen adaylarının dinamik geometri yazılımı ile desteklenmiş ortamda problem kurma durumlarının ve görüşlerinin incelenmesi [Problem posing situations and opinions of pre-service elementary mathematics teachers' in dynamic geometry environment] (Unpublished master's thesis). Gazi University, Institute of Education Sciences, Ankara.

Kar, T. (2014). Ortaokul matematik öğretmenlerinin öğretim için matematiksel bilgisinin problem kurma bağlamında incelenmesi: Kesirlerle toplama işlemi örneği [Investigating middle school mathematics teachers' mathematical knowledge for teaching in the context of problem posing: the example of addition operation with fractions] (Unpublished doctoral dissertation). Atatürk University, Institute of Education Sciences, Erzurum.

Kar, T., & Işık, C. (2015). İlköğretim matematik öğretmenlerinin öğrencilerin kurdukları problemlere yönelik görüşlerinin incelenmesi: kesirlerle toplama işlemi [The investigation of elementary mathematics teachers’ views about problems posed by students: addition operation with fractions]. Hacettepe University Journal of Education, 30(1), 122-136. Kılıç, Ç. (2013). Determining the performances of pre-service primary school teachers in problem posing situations. Educational Sciences: Theory & Practice, 13(2), 1207-1211.

Kırnap-Dönmez, M. S. (2014). İlköğretim matematik öğretmen adaylarının problem kurma becerilerinin incelenmesi [Investigation of problem posing skills of prospective elementary school mathematics teachers] (Unpublished master's thesis). Erciyes University, Institute of Education Sciences, Kayseri. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). New Jersey, Lawrence Erlbaum Associates, Inc.

Lavy, I., & Bershadsky, I. (2003). Problem posing via “what if not?” strategy in solid geometry—A case study. The Journal of Mathematical Behavior, 22(4), 369–387.

Lavy, I., & Shriki, A. (2010). Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. The Journal of Mathematical Behavior, 29(1), 11-24. doi: 10.1016/j.jmathb.2009.12.002

Leikin, R. (2015). Problem posing for and through investigations in a dynamic geometry environment. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 373-391). New York (NY): Springer.

Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5-24.

Lin, K. M., & Leng, L. W. (2008). Using problem posing as an assessment tool. Paper presented at 10th Asia-Pacific Conference on Giftedness, Singapore.

Miles, M. B., & Huberman, A. M. (1994). An expanded source book: Qualitative data analysis. London: Sage Publications.

Nardone, C. F., & Lee R. G. (2011). Critical Inquiry Across Disciplines: Strategies for Student-Generated Problem Posing. College Teaching, 59(1), 13-22.

Ngah, N., Ismail, Z., Tasir, Z., & Mohamad Said, M. N. H. (2016). Students’ ability in free, semi-structured and structured problem posing situations. Advanced Science Letters, 22(12), 4205-4208.

Olkun, S., & Toluk-Uçar, Z. (2014). İlköğretimde etkinlik temelli matematik öğretimi (6. baskı) [Activity based mathematics teaching in primary education (6th ed.)]. Ankara: Eğiten Kitap.

Özdişçi, S., & Kaba, Y. (2018). Investigation of middle school students’ problem solving and problem posing skills. Paper presented at the 27th International Conference on Educational Sciences (April 18-22, 2018), Antalya. It was obtained from http://ices-uebk.org/?s=0.

Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi [Investigation of problem posing skills of eighth grade students in terms of some variables]. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(2), 323-351. DOI: 10.16949/turkbilmat.322660

Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2019). An investigation of eighth grade students’ skills in problem posing. International Journal For Mathematics Teaching And Learning, 20(1), 106-130.

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.

Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing. International Journal of Mathematical Education in Science and Technology, 48(2), 163-184.

Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75-80.

Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school. Journal for Research in Mathematics Education, 27, 521-539.

Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing, Teaching Children Mathematics, 12(3), 129-135.

Singer, F. M., Voica, C., & Pelczer, I. (2017). Cognitive styles in posing geometry problems: Implications for assessment of mathematical creativity. ZDM Mathematics Education, 49(1), 37–52. https://doi.org/10.1007/s11858-016-0820-x

Stoyanova, E. (1997). Extending and exploring students’ problem solving via problem posing: A study of years 8 and 9 students involved in mathematics challenge and enrichment stages of Euler enrichment program for young Australians. Unpublished doctoral dissertation submitted to Edith Cowan University, Perth, Australia.

Stoyanova, E. (2005). Problem posing strategies used by years 8 and 9 students. Australian Mathematics Teacher, 61(3), 6-11.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp.518–525), Melbourne: Mathematics Education Research Group of Australasia.

Şengül, S., & Katrancı, Y. (2012). Problem solving and problem posing skills of prospective mathematics teachers about the ‘sets’ subject. Procedia - Social and Behavioral Sciences, 69, 1650–1655.

Şengül-Akdemir, T., & Türnüklü, E. (2017). Ortaokul 6. sınıf öğrencilerinin açılar ile ilgili problem kurma süreçlerinin incelenmesi [The investigation of 6th grade students’ problem posing processes on angles]. International Journal of New Trends in Arts, Sports & Science Education, 6(2), 17-39.

Tichá, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 1941-1950). Lyon: Institut National de Recherche Pédagogique.

Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.

Turhan, B., & Güven, M. (2014). Problem kurma yaklaşımıyla gerçekleştirilen matematik öğretiminin problem çözme başarısı, problem kurma becerisi ve matematiğe yönelik görüşlere etkisi [The effect of mathematics ınstruction with problem posing approach on problem solving success, problem posing ability and views towards mathematics]. Cukurova University Faculty of Education Journal, 43(2), 217-234.

Türnüklü, E., Ergin, A. S., & Aydoğdu, M. Z. (2017). 8. sınıf öğrencilerinin üçgenler konusunda problem kurma çalışmalarının incelenmesi [Investigation of studies an 8th grade students’ problem posing about triangles]. Journal of Bayburt Education Faculty, 12(24), 467-486.

Ünlü, M., & Aktaş, G. S. (2017). İlköğretim matematik öğretmen adaylarının problem kurma özyeterlik ve problem çözmeye yönelik inançları [Examination of pre-service elementary mathematics teachers’ problems posed about algebraic expressions and equations]. Turkish Journal of Computer and Mathematics Education, 8(1), 161-187.

Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri (10. baskı) [Qualitative Research Methods in the Social Sciences (10th ed.)]. Ankara: Seçkin Yayıncılık.

Yıldız, Z., & Özdemir, A. Ş. (2015). Ortaokul Matematik Öğretmen Adaylarının Problem Kurma Becerilerinin Analizi [Analyzing of problem posing abilities of preservice middle school mathematics teachers]. International Online Journal of Educational Sciences, 7(2), 130-141.

Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5-28). Rotterdam: Sense Publishers.

## Downloads

## Published

## How to Cite

*International Journal of Contemporary Educational Research*,

*7*(1), 1–17. https://doi.org/10.33200/ijcer.575063

## Issue

## Section

## License

Copyright (c) 2022 Mehmet Ertürk Geçici, Mehmet AYDIN

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.